980 lines
25 KiB
C
980 lines
25 KiB
C
#include <math.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
#include <stdio.h>
|
|
#include <complex.h>
|
|
#ifdef complex
|
|
#undef complex
|
|
#endif
|
|
#ifdef I
|
|
#undef I
|
|
#endif
|
|
|
|
#if defined(_WIN64)
|
|
typedef long long BLASLONG;
|
|
typedef unsigned long long BLASULONG;
|
|
#else
|
|
typedef long BLASLONG;
|
|
typedef unsigned long BLASULONG;
|
|
#endif
|
|
|
|
#ifdef LAPACK_ILP64
|
|
typedef BLASLONG blasint;
|
|
#if defined(_WIN64)
|
|
#define blasabs(x) llabs(x)
|
|
#else
|
|
#define blasabs(x) labs(x)
|
|
#endif
|
|
#else
|
|
typedef int blasint;
|
|
#define blasabs(x) abs(x)
|
|
#endif
|
|
|
|
typedef blasint integer;
|
|
|
|
typedef unsigned int uinteger;
|
|
typedef char *address;
|
|
typedef short int shortint;
|
|
typedef float real;
|
|
typedef double doublereal;
|
|
typedef struct { real r, i; } complex;
|
|
typedef struct { doublereal r, i; } doublecomplex;
|
|
#ifdef _MSC_VER
|
|
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
|
|
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
|
|
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
|
|
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
|
|
#else
|
|
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
|
|
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
|
|
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
|
|
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
|
|
#endif
|
|
#define pCf(z) (*_pCf(z))
|
|
#define pCd(z) (*_pCd(z))
|
|
typedef int logical;
|
|
typedef short int shortlogical;
|
|
typedef char logical1;
|
|
typedef char integer1;
|
|
|
|
#define TRUE_ (1)
|
|
#define FALSE_ (0)
|
|
|
|
/* Extern is for use with -E */
|
|
#ifndef Extern
|
|
#define Extern extern
|
|
#endif
|
|
|
|
/* I/O stuff */
|
|
|
|
typedef int flag;
|
|
typedef int ftnlen;
|
|
typedef int ftnint;
|
|
|
|
/*external read, write*/
|
|
typedef struct
|
|
{ flag cierr;
|
|
ftnint ciunit;
|
|
flag ciend;
|
|
char *cifmt;
|
|
ftnint cirec;
|
|
} cilist;
|
|
|
|
/*internal read, write*/
|
|
typedef struct
|
|
{ flag icierr;
|
|
char *iciunit;
|
|
flag iciend;
|
|
char *icifmt;
|
|
ftnint icirlen;
|
|
ftnint icirnum;
|
|
} icilist;
|
|
|
|
/*open*/
|
|
typedef struct
|
|
{ flag oerr;
|
|
ftnint ounit;
|
|
char *ofnm;
|
|
ftnlen ofnmlen;
|
|
char *osta;
|
|
char *oacc;
|
|
char *ofm;
|
|
ftnint orl;
|
|
char *oblnk;
|
|
} olist;
|
|
|
|
/*close*/
|
|
typedef struct
|
|
{ flag cerr;
|
|
ftnint cunit;
|
|
char *csta;
|
|
} cllist;
|
|
|
|
/*rewind, backspace, endfile*/
|
|
typedef struct
|
|
{ flag aerr;
|
|
ftnint aunit;
|
|
} alist;
|
|
|
|
/* inquire */
|
|
typedef struct
|
|
{ flag inerr;
|
|
ftnint inunit;
|
|
char *infile;
|
|
ftnlen infilen;
|
|
ftnint *inex; /*parameters in standard's order*/
|
|
ftnint *inopen;
|
|
ftnint *innum;
|
|
ftnint *innamed;
|
|
char *inname;
|
|
ftnlen innamlen;
|
|
char *inacc;
|
|
ftnlen inacclen;
|
|
char *inseq;
|
|
ftnlen inseqlen;
|
|
char *indir;
|
|
ftnlen indirlen;
|
|
char *infmt;
|
|
ftnlen infmtlen;
|
|
char *inform;
|
|
ftnint informlen;
|
|
char *inunf;
|
|
ftnlen inunflen;
|
|
ftnint *inrecl;
|
|
ftnint *innrec;
|
|
char *inblank;
|
|
ftnlen inblanklen;
|
|
} inlist;
|
|
|
|
#define VOID void
|
|
|
|
union Multitype { /* for multiple entry points */
|
|
integer1 g;
|
|
shortint h;
|
|
integer i;
|
|
/* longint j; */
|
|
real r;
|
|
doublereal d;
|
|
complex c;
|
|
doublecomplex z;
|
|
};
|
|
|
|
typedef union Multitype Multitype;
|
|
|
|
struct Vardesc { /* for Namelist */
|
|
char *name;
|
|
char *addr;
|
|
ftnlen *dims;
|
|
int type;
|
|
};
|
|
typedef struct Vardesc Vardesc;
|
|
|
|
struct Namelist {
|
|
char *name;
|
|
Vardesc **vars;
|
|
int nvars;
|
|
};
|
|
typedef struct Namelist Namelist;
|
|
|
|
#define abs(x) ((x) >= 0 ? (x) : -(x))
|
|
#define dabs(x) (fabs(x))
|
|
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
|
|
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
|
|
#define dmin(a,b) (f2cmin(a,b))
|
|
#define dmax(a,b) (f2cmax(a,b))
|
|
#define bit_test(a,b) ((a) >> (b) & 1)
|
|
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
|
|
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
|
|
|
|
#define abort_() { sig_die("Fortran abort routine called", 1); }
|
|
#define c_abs(z) (cabsf(Cf(z)))
|
|
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
|
|
#ifdef _MSC_VER
|
|
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
|
|
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
|
|
#else
|
|
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
|
|
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
|
|
#endif
|
|
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
|
|
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
|
|
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
|
|
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
|
|
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
|
|
#define d_abs(x) (fabs(*(x)))
|
|
#define d_acos(x) (acos(*(x)))
|
|
#define d_asin(x) (asin(*(x)))
|
|
#define d_atan(x) (atan(*(x)))
|
|
#define d_atn2(x, y) (atan2(*(x),*(y)))
|
|
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
|
|
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
|
|
#define d_cos(x) (cos(*(x)))
|
|
#define d_cosh(x) (cosh(*(x)))
|
|
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
|
|
#define d_exp(x) (exp(*(x)))
|
|
#define d_imag(z) (cimag(Cd(z)))
|
|
#define r_imag(z) (cimagf(Cf(z)))
|
|
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
|
|
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
|
|
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
|
|
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
|
|
#define d_log(x) (log(*(x)))
|
|
#define d_mod(x, y) (fmod(*(x), *(y)))
|
|
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
|
|
#define d_nint(x) u_nint(*(x))
|
|
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
|
|
#define d_sign(a,b) u_sign(*(a),*(b))
|
|
#define r_sign(a,b) u_sign(*(a),*(b))
|
|
#define d_sin(x) (sin(*(x)))
|
|
#define d_sinh(x) (sinh(*(x)))
|
|
#define d_sqrt(x) (sqrt(*(x)))
|
|
#define d_tan(x) (tan(*(x)))
|
|
#define d_tanh(x) (tanh(*(x)))
|
|
#define i_abs(x) abs(*(x))
|
|
#define i_dnnt(x) ((integer)u_nint(*(x)))
|
|
#define i_len(s, n) (n)
|
|
#define i_nint(x) ((integer)u_nint(*(x)))
|
|
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
|
|
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
|
|
#define pow_si(B,E) spow_ui(*(B),*(E))
|
|
#define pow_ri(B,E) spow_ui(*(B),*(E))
|
|
#define pow_di(B,E) dpow_ui(*(B),*(E))
|
|
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
|
|
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
|
|
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
|
|
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
|
|
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
|
|
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
|
|
#define sig_die(s, kill) { exit(1); }
|
|
#define s_stop(s, n) {exit(0);}
|
|
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
|
|
#define z_abs(z) (cabs(Cd(z)))
|
|
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
|
|
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
|
|
#define myexit_() break;
|
|
#define mycycle() continue;
|
|
#define myceiling(w) {ceil(w)}
|
|
#define myhuge(w) {HUGE_VAL}
|
|
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
|
|
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
|
|
|
|
/* procedure parameter types for -A and -C++ */
|
|
|
|
#define F2C_proc_par_types 1
|
|
#ifdef __cplusplus
|
|
typedef logical (*L_fp)(...);
|
|
#else
|
|
typedef logical (*L_fp)();
|
|
#endif
|
|
|
|
static float spow_ui(float x, integer n) {
|
|
float pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
static double dpow_ui(double x, integer n) {
|
|
double pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#ifdef _MSC_VER
|
|
static _Fcomplex cpow_ui(complex x, integer n) {
|
|
complex pow={1.0,0.0}; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow.r *= x.r, pow.i *= x.i;
|
|
if(u >>= 1) x.r *= x.r, x.i *= x.i;
|
|
else break;
|
|
}
|
|
}
|
|
_Fcomplex p={pow.r, pow.i};
|
|
return p;
|
|
}
|
|
#else
|
|
static _Complex float cpow_ui(_Complex float x, integer n) {
|
|
_Complex float pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#endif
|
|
#ifdef _MSC_VER
|
|
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
|
|
_Dcomplex pow={1.0,0.0}; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
|
|
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
|
|
else break;
|
|
}
|
|
}
|
|
_Dcomplex p = {pow._Val[0], pow._Val[1]};
|
|
return p;
|
|
}
|
|
#else
|
|
static _Complex double zpow_ui(_Complex double x, integer n) {
|
|
_Complex double pow=1.0; unsigned long int u;
|
|
if(n != 0) {
|
|
if(n < 0) n = -n, x = 1/x;
|
|
for(u = n; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
#endif
|
|
static integer pow_ii(integer x, integer n) {
|
|
integer pow; unsigned long int u;
|
|
if (n <= 0) {
|
|
if (n == 0 || x == 1) pow = 1;
|
|
else if (x != -1) pow = x == 0 ? 1/x : 0;
|
|
else n = -n;
|
|
}
|
|
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
|
|
u = n;
|
|
for(pow = 1; ; ) {
|
|
if(u & 01) pow *= x;
|
|
if(u >>= 1) x *= x;
|
|
else break;
|
|
}
|
|
}
|
|
return pow;
|
|
}
|
|
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
|
|
{
|
|
double m; integer i, mi;
|
|
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
|
|
if (w[i-1]>m) mi=i ,m=w[i-1];
|
|
return mi-s+1;
|
|
}
|
|
static integer smaxloc_(float *w, integer s, integer e, integer *n)
|
|
{
|
|
float m; integer i, mi;
|
|
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
|
|
if (w[i-1]>m) mi=i ,m=w[i-1];
|
|
return mi-s+1;
|
|
}
|
|
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b CGEBAL */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGEBAL + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebal.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebal.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebal.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) */
|
|
|
|
/* CHARACTER JOB */
|
|
/* INTEGER IHI, ILO, INFO, LDA, N */
|
|
/* REAL SCALE( * ) */
|
|
/* COMPLEX A( LDA, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGEBAL balances a general complex matrix A. This involves, first, */
|
|
/* > permuting A by a similarity transformation to isolate eigenvalues */
|
|
/* > in the first 1 to ILO-1 and last IHI+1 to N elements on the */
|
|
/* > diagonal; and second, applying a diagonal similarity transformation */
|
|
/* > to rows and columns ILO to IHI to make the rows and columns as */
|
|
/* > close in norm as possible. Both steps are optional. */
|
|
/* > */
|
|
/* > Balancing may reduce the 1-norm of the matrix, and improve the */
|
|
/* > accuracy of the computed eigenvalues and/or eigenvectors. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > Specifies the operations to be performed on A: */
|
|
/* > = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
|
|
/* > for i = 1,...,N; */
|
|
/* > = 'P': permute only; */
|
|
/* > = 'S': scale only; */
|
|
/* > = 'B': both permute and scale. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > On entry, the input matrix A. */
|
|
/* > On exit, A is overwritten by the balanced matrix. */
|
|
/* > If JOB = 'N', A is not referenced. */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > \param[out] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > ILO and IHI are set to integers such that on exit */
|
|
/* > A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
|
|
/* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is REAL array, dimension (N) */
|
|
/* > Details of the permutations and scaling factors applied to */
|
|
/* > A. If P(j) is the index of the row and column interchanged */
|
|
/* > with row and column j and D(j) is the scaling factor */
|
|
/* > applied to row and column j, then */
|
|
/* > SCALE(j) = P(j) for j = 1,...,ILO-1 */
|
|
/* > = D(j) for j = ILO,...,IHI */
|
|
/* > = P(j) for j = IHI+1,...,N. */
|
|
/* > The order in which the interchanges are made is N to IHI+1, */
|
|
/* > then 1 to ILO-1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexGEcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The permutations consist of row and column interchanges which put */
|
|
/* > the matrix in the form */
|
|
/* > */
|
|
/* > ( T1 X Y ) */
|
|
/* > P A P = ( 0 B Z ) */
|
|
/* > ( 0 0 T2 ) */
|
|
/* > */
|
|
/* > where T1 and T2 are upper triangular matrices whose eigenvalues lie */
|
|
/* > along the diagonal. The column indices ILO and IHI mark the starting */
|
|
/* > and ending columns of the submatrix B. Balancing consists of applying */
|
|
/* > a diagonal similarity transformation inv(D) * B * D to make the */
|
|
/* > 1-norms of each row of B and its corresponding column nearly equal. */
|
|
/* > The output matrix is */
|
|
/* > */
|
|
/* > ( T1 X*D Y ) */
|
|
/* > ( 0 inv(D)*B*D inv(D)*Z ). */
|
|
/* > ( 0 0 T2 ) */
|
|
/* > */
|
|
/* > Information about the permutations P and the diagonal matrix D is */
|
|
/* > returned in the vector SCALE. */
|
|
/* > */
|
|
/* > This subroutine is based on the EISPACK routine CBAL. */
|
|
/* > */
|
|
/* > Modified by Tzu-Yi Chen, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int cgebal_(char *job, integer *n, complex *a, integer *lda,
|
|
integer *ilo, integer *ihi, real *scale, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
|
real r__1, r__2;
|
|
|
|
/* Local variables */
|
|
integer iexc;
|
|
real c__, f, g;
|
|
integer i__, j, k, l, m;
|
|
real r__, s;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
|
|
complex *, integer *);
|
|
real sfmin1, sfmin2, sfmax1, sfmax2, ca;
|
|
extern real scnrm2_(integer *, complex *, integer *);
|
|
real ra;
|
|
extern integer icamax_(integer *, complex *, integer *);
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
|
|
*), xerbla_(char *, integer *, ftnlen);
|
|
extern logical sisnan_(real *);
|
|
logical noconv;
|
|
integer ica, ira;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--scale;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
|
|
&& ! lsame_(job, "B")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -4;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CGEBAL", &i__1, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
k = 1;
|
|
l = *n;
|
|
|
|
if (*n == 0) {
|
|
goto L210;
|
|
}
|
|
|
|
if (lsame_(job, "N")) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
scale[i__] = 1.f;
|
|
/* L10: */
|
|
}
|
|
goto L210;
|
|
}
|
|
|
|
if (lsame_(job, "S")) {
|
|
goto L120;
|
|
}
|
|
|
|
/* Permutation to isolate eigenvalues if possible */
|
|
|
|
goto L50;
|
|
|
|
/* Row and column exchange. */
|
|
|
|
L20:
|
|
scale[m] = (real) j;
|
|
if (j == m) {
|
|
goto L30;
|
|
}
|
|
|
|
cswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
|
|
i__1 = *n - k + 1;
|
|
cswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
|
|
|
|
L30:
|
|
switch (iexc) {
|
|
case 1: goto L40;
|
|
case 2: goto L80;
|
|
}
|
|
|
|
/* Search for rows isolating an eigenvalue and push them down. */
|
|
|
|
L40:
|
|
if (l == 1) {
|
|
goto L210;
|
|
}
|
|
--l;
|
|
|
|
L50:
|
|
for (j = l; j >= 1; --j) {
|
|
|
|
i__1 = l;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (i__ == j) {
|
|
goto L60;
|
|
}
|
|
i__2 = j + i__ * a_dim1;
|
|
if (a[i__2].r != 0.f || r_imag(&a[j + i__ * a_dim1]) != 0.f) {
|
|
goto L70;
|
|
}
|
|
L60:
|
|
;
|
|
}
|
|
|
|
m = l;
|
|
iexc = 1;
|
|
goto L20;
|
|
L70:
|
|
;
|
|
}
|
|
|
|
goto L90;
|
|
|
|
/* Search for columns isolating an eigenvalue and push them left. */
|
|
|
|
L80:
|
|
++k;
|
|
|
|
L90:
|
|
i__1 = l;
|
|
for (j = k; j <= i__1; ++j) {
|
|
|
|
i__2 = l;
|
|
for (i__ = k; i__ <= i__2; ++i__) {
|
|
if (i__ == j) {
|
|
goto L100;
|
|
}
|
|
i__3 = i__ + j * a_dim1;
|
|
if (a[i__3].r != 0.f || r_imag(&a[i__ + j * a_dim1]) != 0.f) {
|
|
goto L110;
|
|
}
|
|
L100:
|
|
;
|
|
}
|
|
|
|
m = k;
|
|
iexc = 2;
|
|
goto L20;
|
|
L110:
|
|
;
|
|
}
|
|
|
|
L120:
|
|
i__1 = l;
|
|
for (i__ = k; i__ <= i__1; ++i__) {
|
|
scale[i__] = 1.f;
|
|
/* L130: */
|
|
}
|
|
|
|
if (lsame_(job, "P")) {
|
|
goto L210;
|
|
}
|
|
|
|
/* Balance the submatrix in rows K to L. */
|
|
|
|
/* Iterative loop for norm reduction */
|
|
|
|
sfmin1 = slamch_("S") / slamch_("P");
|
|
sfmax1 = 1.f / sfmin1;
|
|
sfmin2 = sfmin1 * 2.f;
|
|
sfmax2 = 1.f / sfmin2;
|
|
L140:
|
|
noconv = FALSE_;
|
|
|
|
i__1 = l;
|
|
for (i__ = k; i__ <= i__1; ++i__) {
|
|
|
|
i__2 = l - k + 1;
|
|
c__ = scnrm2_(&i__2, &a[k + i__ * a_dim1], &c__1);
|
|
i__2 = l - k + 1;
|
|
r__ = scnrm2_(&i__2, &a[i__ + k * a_dim1], lda);
|
|
ica = icamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
|
|
ca = c_abs(&a[ica + i__ * a_dim1]);
|
|
i__2 = *n - k + 1;
|
|
ira = icamax_(&i__2, &a[i__ + k * a_dim1], lda);
|
|
ra = c_abs(&a[i__ + (ira + k - 1) * a_dim1]);
|
|
|
|
/* Guard against zero C or R due to underflow. */
|
|
|
|
if (c__ == 0.f || r__ == 0.f) {
|
|
goto L200;
|
|
}
|
|
g = r__ / 2.f;
|
|
f = 1.f;
|
|
s = c__ + r__;
|
|
L160:
|
|
/* Computing MAX */
|
|
r__1 = f2cmax(f,c__);
|
|
/* Computing MIN */
|
|
r__2 = f2cmin(r__,g);
|
|
if (c__ >= g || f2cmax(r__1,ca) >= sfmax2 || f2cmin(r__2,ra) <= sfmin2) {
|
|
goto L170;
|
|
}
|
|
r__1 = c__ + f + ca + r__ + g + ra;
|
|
if (sisnan_(&r__1)) {
|
|
|
|
/* Exit if NaN to avoid infinite loop */
|
|
|
|
*info = -3;
|
|
i__2 = -(*info);
|
|
xerbla_("CGEBAL", &i__2, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
f *= 2.f;
|
|
c__ *= 2.f;
|
|
ca *= 2.f;
|
|
r__ /= 2.f;
|
|
g /= 2.f;
|
|
ra /= 2.f;
|
|
goto L160;
|
|
|
|
L170:
|
|
g = c__ / 2.f;
|
|
L180:
|
|
/* Computing MIN */
|
|
r__1 = f2cmin(f,c__), r__1 = f2cmin(r__1,g);
|
|
if (g < r__ || f2cmax(r__,ra) >= sfmax2 || f2cmin(r__1,ca) <= sfmin2) {
|
|
goto L190;
|
|
}
|
|
f /= 2.f;
|
|
c__ /= 2.f;
|
|
g /= 2.f;
|
|
ca /= 2.f;
|
|
r__ *= 2.f;
|
|
ra *= 2.f;
|
|
goto L180;
|
|
|
|
/* Now balance. */
|
|
|
|
L190:
|
|
if (c__ + r__ >= s * .95f) {
|
|
goto L200;
|
|
}
|
|
if (f < 1.f && scale[i__] < 1.f) {
|
|
if (f * scale[i__] <= sfmin1) {
|
|
goto L200;
|
|
}
|
|
}
|
|
if (f > 1.f && scale[i__] > 1.f) {
|
|
if (scale[i__] >= sfmax1 / f) {
|
|
goto L200;
|
|
}
|
|
}
|
|
g = 1.f / f;
|
|
scale[i__] *= f;
|
|
noconv = TRUE_;
|
|
|
|
i__2 = *n - k + 1;
|
|
csscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
|
|
csscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);
|
|
|
|
L200:
|
|
;
|
|
}
|
|
|
|
if (noconv) {
|
|
goto L140;
|
|
}
|
|
|
|
L210:
|
|
*ilo = k;
|
|
*ihi = l;
|
|
|
|
return 0;
|
|
|
|
/* End of CGEBAL */
|
|
|
|
} /* cgebal_ */
|
|
|